If e cos 2 x + cos 4 x + cos 6 x + . . . . ∞ log e 2 satisfies the equation t 2 - 9 t + 8 = 0 , then the value of 2 sin x sin x + 3 cos x , where 0 < x < π 2 , is equal to

Question

If e cos 2 x + cos 4 x + cos 6 x + . . . . &#8734; log e 2 satisfies the equation t 2 - 9 t + 8 = 0 , then the value of 2 sin x sin x + 3 cos x , where 0 &#60; x &#60; &#960; 2 , is equal to

Aicharya · Accepted Answer

e cos 2 x + cos 4 x + &#8230; &#8230; &#8734; ln &#160; 2 = 2 cos 2 x + cos 4 x + &#8230; &#8230; &#8734; = = 2 cos 2 x 1 - cos 2 x = 2 cot 2 x t 2 - 9 t + 8 = 0 &#8658; t = 1 , 8 &#8658; 2 cot 2 x = 1 , &#160; 8 &#8658; cot 2 x = 0 , 3 0 &#60; x &#60; &#960; 2 &#8658; cot &#160; x = 3 &#8658; 2 &#160; sin &#160; x sin &#160; x + 3 &#160; cos &#160; x = 2 1 + 3 &#160; cot &#160; x = 2 4 = 1 2

If e cos 2 x + cos 4 x + cos 6 x + . . . . ∞ log e 2 satisfies the equation t 2 - 9 t + 8 = 0 , then…

Solution

If e cos 2 x + cos 4 x + cos 6 x + . . . . &#8734; log e 2 satisfies the equation t 2 - 9 t + 8 = 0 , then…

Solution

If e cos 2 x + cos 4 x + cos 6 x + . . . . ∞ log e 2 satisfies the equation t 2 - 9 t + 8 = 0 , then…